Solve 7x^-3*4x^-2

$$7 x ^ { - 3 } \cdot 4 x ^ { - 2 }$$

Evaluate

$$\frac{28}{x^{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$7x^{-5}\times 4$$

Multiply 7 and 4 to get 28.

$$28x^{-5}$$

Differentiate w.r.t. x

$$-\frac{140}{x^{6}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and -2 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{-5}\times 4)$$

Multiply 7 and 4 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}x}(28x^{-5})$$

The derivative of ax^{n} is nax^{n-1}.

$$-5\times 28x^{-5-1}$$

Multiply -5 times 28.

$$-140x^{-5-1}$$

Subtract 1 from -5.

$$-140x^{-6}$$